For what its worth (only just found this) here is my take on this.
I have a 17 yr lad that got into mountain biking about 2 years ago now.
He now has 2 bikes a 29er hard tail and a full sus both of which we have built together - something initialy new to both of us.
To fund this we have let him use what savings he has and I have assisted in the pruchases here and there, but not excessively; its a tricky balance between wanting to enourage an interest/pursuit and not spoil - this period of time only cones around once you can't repeat.
He has also funded alot of bike improvements by selling on ebay including his PSP - result! Though suspect the PS3 will never be sacrificed.
I am a keen mountain walker and have had a mountain bike of sorts for years .... like 25 (Kona Cider Cone no suspension lovely speckled paint job). I have also invested in a decent bike and upgraded it - mainly to keep up and be safe.
Together we have been to many trail centres including in the last 2 summers 4 week long trips up to Scotland where possible taking a friend. I have also tried to get him to into some longer XC routes e.g Gap over the Beacons.
I think the main points here are to get them into bike maintenance & building - gives skills, knowledge, confidence. Does not have to be expensive, 100s not 1000s required. If they want to spend more .... get a job. Helps if they have a mate or club they can use - going with dad is last resort and I can't keep up now especially as he appears to be moving from red to black routes now.
Going back to original thread point which is perhaps if to assist/spend on something that may just be the latest thing, you can only judge that yourselve, but guess I would go for encourage with reserve. At the end of the day we want to get them off that console and outside!